For detailed proof, we refer to [1]}.

Thanks to res: ChFInversionTheorem, we have that if \(\phi _A\)  is analytic, so it is \(F_A\)  (as long as the integral in (REF ) is well defined).
Thus, the problem becomes to determine if \(\phi _A\)  is analytic. We rely on a characterization of entireEntire functions are complex analytic functions in the whole complex plan \(\mathbb { C}\) . ChFs, which can be used in this framework to show that in the cases of – fixed- or float-strike – discrete arithmetic Asian and Lookback options, the (complex extension of the) function \(\phi _A\)  is analytic in a certain domain.
